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422 The analytic hierarchy process
that AHP questions, which simply ask for the relative importance of
attributes without reference to their scales, imply weights that reflect
the relative value of the average score of the options on the different
criteria, 9 which is a difficult concept for decision makers to conceive.
This may mean that the questions are interpreted in different, and
possibly erroneous, ways by decision makers. 9,10
(4) New alternatives can reverse the rank of existing alternatives. This issue,
which is related to the last point, has attracted much attention.
Suppose that you are using the AHP to choose a location for a new
sales office and the weights you obtained from the method give the
following order of preference: 1. Albuquerque, 2. Boston, 3. Chicago.
However, before making the decision you discover that a site in
Denver is also worth considering so you repeat the AHP to include
this new option. Even though you leave the relative importance
of the attributes unchanged, the new analysis gives the following
rankings: 1. Boston, 2. Albuquerque, 3. Denver, 4. Chicago, so the
rank of Albuquerque and Boston has been reversed, which does not
seem to be intuitively reasonable. Belton and Gear 11 showed that
this arises from the way in which the AHP normalizes the weights
to sum to 1. They went on to show that this is consistent with a
definition of weights which is at variance with that used in SMART
(see above). Most decision makers, they argued, would consider the
SMART definition to be the reasonable one.
(5) Number of comparisons required may be large. While the redundancy
built into the AHP is an advantage, it may also require a large number
of judgments from the decision maker. Consider, for example, the
office location problem in Chapter 3, which involved 7 alternatives
and 7 attributes (if we simplify the problem to include ‘Total Costs’
and only lower-level benefit attributes). This would involve 168
pairwise comparisons of importance or preference. In a study by
Olson et al. 10 this requirement to answer a large number of questions
reduced the attraction of the AHP in the eyes of potential users, even
though the questions themselves were considered to be easy.
(6) The axioms of the method. As we saw in Chapter 3, SMART is well
founded on a set of axioms, that is, a set of rules which are intended
to provide the basis for rational decision making. Dyer 12 has argued
that the clarity and intuitive meaning of these axioms allows their
appeal, as rules for rational behavior to be debated and empirically
tested. In contrast, he argues, the axioms of the AHP 3 are not
founded on testable descriptions of rational behavior (see Harker
and Vargas 13 for a reply to Dyer’s paper).